where \({u}^{FOM}\)  is the FOM solution, \({u}^{ROM}\)  is the ROM solution, \(\Vert  \cdot \Vert \)  is a given norm, the space error is the error that results from the spatial approximation, the time error is the error that results from the time approximation, the ROM error is the error that results from the ROM approximation, and \(C\)  is a generic constant that does not depend on the discretization parameters.
We note that the first two terms on the right-hand side of (REF ) appear in error bounds for classical numerical discretizations, e.g., the FEM [1]}.
The third term, however, does not appear in these bounds.
